Related papers: Intrinsic Chirality of Multipartite Graphs
A classification is given of all the countable homogeneous ordered bipartite graphs.
Molecular chirality is actively researched in a variety of areas of biology, including biochemistry, physiology, pharmacology, etc., and today many chiral compounds are widely known to exhibit biological properties. The molecular structure…
In this note we give a combinatorial characterization of all the unmixed bipartite graphs.
We derive a formula for the QE constant of a complete multipartite graph and determine the complete multipartite graphs of non-QE class, namely, those which do not admit quadratic embeddings in a Euclidean space. Moreover, the primary…
It is well known that the complete multipartite graphs can not be determined by their adjacency spectra. But in this paper, we prove that they can be determined by their distance spectra, which confirms the conjecture proposed by Lin, Hong,…
In this paper we consider bi-Cohen-Macaulay graphs, and give a complete classification of such graphs in the case they are bipartite or chordal. General bi-Cohen-Macaulay graphs are classified up to separation. The inseparable…
In this paper we determine all the bipartite graphs with the maximum sum of squares of degrees among the ones with a given number of vertices and edges.
Motivated by the concept of well-covered graphs, we define a graph to be well-bicovered if every vertex-maximal bipartite subgraph has the same order (which we call the bipartite number). We first give examples of them, compare them with…
Extending the work of Godsil and others, we investigate the notion of the inverse of a graph (specifically, of bipartite graphs with a unique perfect matching). We provide a concise necessary and sufficient condition for the invertibility…
In this paper, we classify the connected non-bipartite integral graphs with spectral radius three.
It is well known that a plane graph is Eulerian if and only if its geometric dual is bipartite. We extend this result to partial duals of plane graphs. We then characterize all bipartite partial duals of a plane graph in terms of oriented…
Motivated by recent extensive studies on Wenger graphs, we introduce a new infinite class of bipartite graphs of the similar type, called linearized Wenger graphs. The spectrum, diameter and girth of these linearized Wenger graphs are…
We consider a set of cliques in any multipartite graph with two vertices in each part. Moreover, we construct a class of peculiar polytopes. Key words: multipartite graph, clique, polytope.
We find all polyhedral graphs such that their complements are still polyhedral. These turn out to be all self-complementary.
We present evidence in support of a conjecture that a bipartite graph with at least five vertices in each part and |E(G)| \geq 4 |V(G)| - 17 is intrinsically knotted. We prove the conjecture for graphs that have exactly five or exactly six…
In this paper, we completely classify the connected non-bipartite graphs with integral signless Laplacian eigenvalues at most 6.
The concept of graph powers has been extensively studied in graph theory. Analogous to graph powers, Chandran et al. [3] introduced the notion of bipartite powers for bipartite graphs. In this paper, we show that the class of interval…
We calculate the cordial edge deficiencies of the complete multipartite graphs and find an upper bound for their cordial vertex deficiencies. We also give conditions under which the tensor product of two cordial graphs is cordial.
We show that if the two parts of a finite bipartite graph have the same degree sequence, then there is a bipartite graph, with the same degree sequences, which is symmetric, in that it has an involutive graph automorphism that interchanges…
We say that a graph is intrinsically non-trivial if every spatial embedding of the graph contains a non-trivial spatial subgraph. We prove that an intrinsically non-trivial graph is intrinsically linked, namely every spatial embedding of…